What is the integral of (5x^4-6x^2+3) ?

The integral of (5x^4-6x^2+3) is x^5-2x^3+3x+C

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integral of (5x^4-6x^2+3)

\int (5 x^{4} - 6 x^{2} + 3) d x

x^{5} - 2 x^{3} + 3 x + C

Solution steps

\int 5 x^{4} - 6 x^{2} + 3 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 5 x^{4} d x - \int 6 x^{2} d x + \int 3 d x

\int 5 x^{4} d x = x^{5}

\int 6 x^{2} d x = 2 x^{3}

\int 3 d x = 3 x

= x^{5} - 2 x^{3} + 3 x

Add a constant to the solution

= x^{5} - 2 x^{3} + 3 x + C

\int \frac{e ^{2 x}}{4 + e ^{2 x}} d x

\frac{d}{d x} (ln (e^{x} + 3))

\int tan (9 x) sec^{\frac{5}{4}} (9 x) d x

x \to \infty lim (x^{2} - 5)

t \to - 3 lim (\frac{t - 2}{t + 5})

What is the integral of (5x^4-6x^2+3) ?
The integral of (5x^4-6x^2+3) is x^5-2x^3+3x+C